1. What is Cot Inverse?

The cot inverse function (arccot) is the inverse of the cotangent function. It returns the angle whose cotangent is the given number. This calculator uses the sine-based formula to compute arccot.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( x \) — Input value (dimensionless)
• \( \arcsin \) — Inverse sine function
• \( \sqrt{1+x^2} \) — Square root term in denominator

Explanation: The formula derives from trigonometric identities and provides an alternative method to calculate arccot using the arcsin function.

3. Mathematical Background

Details: The cot inverse function is defined for all real numbers and returns values in the range (0, π) radians or (0°, 180°). The sine-based approach offers computational advantages in certain scenarios.

4. Using the Calculator

Tips: Enter any real number value for x (except zero). The calculator will return the angle in degrees. Ensure valid numerical input for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: Why use this formula instead of direct arccot?
A: This formula provides an alternative computational method and demonstrates the relationship between inverse trigonometric functions.

Q2: What is the range of arccot values?
A: The arccot function returns values between 0° and 180° (0 and π radians).

Q3: Why can't x be zero?
A: Cotangent is undefined at zero, so arccot(0) is not defined in the real number system.

Q4: How accurate are the results?
A: Results are accurate to 4 decimal places, using PHP's built-in trigonometric functions.

Q5: Can I use negative values for x?
A: Yes, the arccot function accepts all real numbers except zero.